Modern communication systems provide higher rates of data transmission through the use of multiple-level modulation such as M-ary quadrature amplitude modulation (QAM). Although soft input decoders are preferable in many communication systems, most soft input decoders are designed for binary modulation, i.e., a soft bit instead of a multiple-level code symbol. Thus, a method and apparatus for efficiently converting a multiple-level modulation symbol to multiple soft bit inputs for decoders by taking advantage of the inherent structure of such conversion is needed which will provide for better decoder performance and less hardware complexity.
In the prior art, multiple level modulation and coding schemes are jointly and integrally designed such that one modulation symbol can generate a single branch metric for a soft input decoder rather than producing multiple soft bits that can be individually processed. Among these techniques are trellis coded modulation (TCM) and turbo trellis modulation. Unfortunately, such direct conversion of modulation symbol to code symbol is not desirable in most wireless communication systems that require an interleaver between the modulation symbol demapper and the channel encoder as shown in FIG. 1. Since in wireless communication systems a fading channel often causes burst errors, the output of the channel encoder should be interleaved before being mapped to modulation symbols. This requires the receiver to decompose a modulation symbol into multiple soft input bits so that the soft bits may be deinterleaved and inputted to the decoder as shown in FIG. 1.
The following example is described in the context of the specific Gray-coded 64-QAM constellation shown in FIG. 2. The example illustrates a prior art technique for converting a received modulation symbol to multiple soft bits.
Each point of the 64-QAM constellation is represented by two real numbers (CIi,CQi) i=1, . . . , 64 and corresponds to input data bits b0b1 . . . b5 . In additive white Gaussian noise channels, it is known that the following log-likelihood ratio produces the optimal conversion from a received modulation symbol (XI,Xq) to soft bit inputs bk k=0, . . . , 5 for use with soft input decoders.                               b          k                =                  log          ⁢                                           ⁢                                                    ∑                                  i                  ∈                                      S                                          +                      k                                                                                  ⁢                              exp                ⁡                                  (                                                            -                                                                                                    (                                                                                          X                                I                                                            -                                                              c                                Ii                                                                                      )                                                    2                                                                          2                          ⁢                                                      σ                            2                                                                                                                -                                                                                            (                                                                                    X                              Q                                                        -                                                          c                              Qi                                                                                )                                                2                                                                    2                        ⁢                                                  σ                          2                                                                                                      )                                                                                    ∑                                  j                  ∈                                      S                                          -                      k                                                                                  ⁢                              exp                ⁡                                  (                                                            -                                                                                                    (                                                                                          X                                I                                                            -                                                              c                                Ij                                                                                      )                                                    2                                                                          2                          ⁢                                                      σ                            2                                                                                                                -                                                                                            (                                                                                    X                              Q                                                        -                                                          c                              Qj                                                                                )                                                2                                                                    2                        ⁢                                                  σ                          2                                                                                                      )                                                                                        Equation  (1)            
Here, σ2 is the noise variance associated with the channel, exp( ) is the exponential function, log( ) is the natural logarithmic function, S+k and S−k are the sets of thirty two constellation points corresponding to the case when the transmitted bit bk is 0 and the case when the transmitted bit is 1, respectively. In the context of a practical communication system, the received modulation symbol quantities (XI, Xq) are obtained by the receiver section, the channel noise is estimated by the receiver section, and the values of c and the modulation symbol constellation are predetermined and known by the receiver section a priori. This log-likelihood ratio calculation requires a significant amount of computation; the complexity of this calculation makes it impractical for use with actual communication systems. To avoid this computation problem, two conventional approximation schmes have been developed: the nearest neighbor Euclidean distance calculation and the progressive decision technique. First, the nearest neighbor Euclidean distance calculation approximates the log likelihood ratio by the following equation:                                                                         b                k                            =                            ⁢                                                1                                      2                    ⁢                                          σ                      2                                                                      [                                                                            min                                              i                        ∈                                                  S                                                      -                            k                                                                                                                ⁢                                          {                                                                                                    (                                                                                          X                                I                                                            -                                                              c                                Ii                                                                                      )                                                    2                                                +                                                                              (                                                                                          X                                Q                                                            -                                                              c                                Qi                                                                                      )                                                    2                                                                    }                                                        -                                                                                                                      ⁢                                                                    min                                          j                      ∈                                              S                                                  +                          k                                                                                                      ⁢                                      {                                                                                            (                                                                                    X                              I                                                        -                                                          c                              Ij                                                                                )                                                2                                            +                                                                        (                                                                                    X                              Q                                                        -                                                          c                              Qj                                                                                )                                                2                                                              }                                                  ]                                                                        Equation  (2)            
In Equation 2, min { } is the minimum function.
The second method further approximates the exact log-likelihood calculation by decoupling the real and imaginary components (XI,Xq) of the modulation symbol and making a plurality of progressive soft decisions, as follows:b0=abs(XI)b1=abs(XQ)b2=abs(b0)−D1b3=abs(b1)−D1b4=abs(b2)−D2b0=abs(b3)−D2   Equation (3)
In the above expressions, abs( ) is the absolute value function and D1 and D2 are specified decision boundaries (for example, 0.617 and 0.308, respectively).
The above-mentioned methods suffer from either excessive computation or performance loss. In other words, although the approximation techniques may be easier to implement, the resulting decoder performance suffers.